Removable sets for continuous solutions of quasilinear elliptic equations

Kilpeläinen, Tero; Zhong, Xiao

doi:10.1090/S0002-9939-01-06237-2

Removable sets for continuous solutions of quasilinear elliptic equations
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by Tero Kilpeläinen and Xiao Zhong PDF

Proc. Amer. Math. Soc. 130 (2002), 1681-1688 Request permission

Abstract:

We show that sets of $n-p+\alpha (p-1)$ Hausdorff measure zero are removable for $\alpha$-Hölder continuous solutions to quasilinear elliptic equations similar to the $p$-Laplacian. The result is optimal. We also treat larger sets in terms of a growth condition. In particular, our results apply to quasiregular mappings.

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